Applying network calculus for performance analysis of self-similar traffic in on-chip networks

On-chip traffic of many applications exhibits self-similar characteristics. In this paper, we intend to apply network calculus to analyze the delay and backlog bounds for self-similar traffic in networks on chips. We first prove that self-similar traffic can not be constrained by any deterministic arrival curve. Then we prove that self-similar traffic can be constrained by deterministic linear arrival curves α{r,b}(t)=rt+b (r:rate, b:burstiness) if an additional parameter, excess probability ε, is used to capture its burstiness exceeding the arrival envelope. This three-parameter model, ε-α{r,b}(t)=rt+b(ε), enables us to apply and extend the results of network calculus to analyze the performance and buffering cost of networks delivering self-similar traffic flows. Assuming the latency-rate server model for the network elements, we give closed-form equations to compute the delay and backlog bounds for self-similar traffic traversing a series of network elements. Furthermore, we describe a performance analysis flow with self-similar traffic as input. Our experimental results using real on-chip multimedia traffic traces validate our model and approach.